Yuki doesn't like saying the brat's name because he feels he's allowing himself to become vulnerable again. He thinks that by saying the brat's name, the idiot will be gone, and while sometimes that is a good thing and though he would never ever admit it, he doesn't want his heart broken again. Yuki thinks it's terrible he's even fallen for the little loser. He thinks it's even more terrible how the idiot even managed to break the cold-hearted shell he has built over his cold-hearted years. Damn that brat and his name.
But what Yuki hates even more than saying the idiot's name is K. Not only because every morning he has to wake up to shots in his ceiling and walls, but because his brat has to have a dancing ballad with Ryuichi fucking Sakuma to 'promote Bad Luck and welcome Ryuichi back to the music world'. Promote, his ass. What Yuki hates more thank K is Ryuichi, but what he hates more than Ryuichi is jealousy, and jealousy makes you vulnerable.
And he hates that.
When the brat told him what K was forcing him to do, Yuki's eyes burned with jealousy.
Not that he'd ever admit that.
Ever.
He'll even show you the exact words. . . .
"Guess what, Yuki! I get to dance with Sakuma-kun! It's a very fast song. We even practiced it today! We're, like, chest to chest close!"
"Oh." Silence. "Leave me alone."
Relying on that, you can't really see Yuki's jealous. But deep inside Yuki's cold-hearted exterior beats the heart of blazing green jealousy.
Not that he'd ever show it.
But with the idiot, it makes him happy to see Yuki express his feelings. So maybe he'll admit it—He's jealous.
And because jealousy means vulnerability, he'll have to say the brat's name.
Shuichi.